Results 1  10
of
39
Robust Higher Order Potentials for Enforcing Label Consistency
, 2009
"... This paper proposes a novel framework for labelling problems which is able to combine multiple segmentations in a principled manner. Our method is based on higher order conditional random fields and uses potentials defined on sets of pixels (image segments) generated using unsupervised segmentation ..."
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Cited by 259 (34 self)
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This paper proposes a novel framework for labelling problems which is able to combine multiple segmentations in a principled manner. Our method is based on higher order conditional random fields and uses potentials defined on sets of pixels (image segments) generated using unsupervised segmentation algorithms. These potentials enforce label consistency in image regions and can be seen as a generalization of the commonly used pairwise contrast sensitive smoothness potentials. The higher order potential functions used in our framework take the form of the Robust P n model and are more general than the P n Potts model recently proposed by Kohli et al. We prove that the optimal swap and expansion moves for energy functions composed of these potentials can be computed by solving a stmincut problem. This enables the use of powerful graph cut based move making algorithms for performing inference in the framework. We test our method on the problem of multiclass object segmentation by augmenting the conventional CRF used for object segmentation with higher order potentials defined on image regions. Experiments on challenging data sets show that integration of higher order potentials quantitatively and qualitatively improves results leading to much better definition of object boundaries. We
Global Stereo Reconstruction under Second Order Smoothness Priors
"... Secondorder priors on the smoothness of 3D surfaces are a better model of typical scenes than firstorder priors. However, stereo reconstruction using global inference algorithms, such as graphcuts, has not been able to incorporate secondorder priors because the triple cliques needed to express t ..."
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Cited by 127 (8 self)
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Secondorder priors on the smoothness of 3D surfaces are a better model of typical scenes than firstorder priors. However, stereo reconstruction using global inference algorithms, such as graphcuts, has not been able to incorporate secondorder priors because the triple cliques needed to express them yield intractable (nonsubmodular) optimization problems. This paper shows that inference with triple cliques can be effectively optimized. Our optimization strategy is a development of recent extensions to αexpansion, based on the “QPBO ” algorithm [5, 14, 26]. The strategy is to repeatedly merge proposal depth maps using a novel extension of QPBO. Proposal depth maps can come from any source, for example frontoparallel planes as in αexpansion, or indeed any existing stereo algorithm, with arbitrary parameter settings. Experimental results demonstrate the usefulness of the secondorder prior and the efficacy of our optimization framework. An implementation of our stereo framework is available online [34].
Beyond pairwise energies: Efficient optimization for higherorder MRFs
 in IEEE Conference on Computer Vision and Pattern Recognition : CVPR
, 2009
"... In this paper, we introduce a higherorder MRF optimization framework. On the one hand, it is very general; we thus use it to derive a generic optimizer that can be applied to almost any higherorder MRF and that provably optimizes a dual relaxation related to the input MRF problem. On the other han ..."
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Cited by 80 (11 self)
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In this paper, we introduce a higherorder MRF optimization framework. On the one hand, it is very general; we thus use it to derive a generic optimizer that can be applied to almost any higherorder MRF and that provably optimizes a dual relaxation related to the input MRF problem. On the other hand, it is also extremely flexible and thus can be easily adapted to yield far more powerful algorithms when dealing with subclasses of highorder MRFs. We thus introduce a new powerful class of highorder potentials, which are shown to offer enough expressive power and to be useful for many vision tasks. To address them, we derive, based on the same framework, a novel and extremely efficient messagepassing algorithm, which goes beyond the aforementioned generic optimizer and is able to deliver almost optimal solutions of very high quality. Experimental results on vision problems demonstrate the extreme effectiveness of our approach. For instance, we show that in some cases we are even able to compute the global optimum for NPhard higherorder MRFs in a very efficient manner. 1.
Exact Inference in Multilabel CRFs with Higher Order Cliques
, 2008
"... This paper addresses the problem of exactly inferring the maximum a posteriori solutions of discrete multilabel MRFs or CRFs with higher order cliques. We present a framework to transform special classes of multilabel higher order functions to submodular second order boolean functions (referred to ..."
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Cited by 50 (11 self)
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This paper addresses the problem of exactly inferring the maximum a posteriori solutions of discrete multilabel MRFs or CRFs with higher order cliques. We present a framework to transform special classes of multilabel higher order functions to submodular second order boolean functions (referred to as F 2 s), which can be minimized exactly using graph cuts and we characterize those classes. The basic idea is to use two or more boolean variables to encode the states of a single multilabel variable. There are many ways in which this can be done and much interesting research lies in finding ways which are optimal or minimal in some sense. We study the space of possible encodings and find the ones that can transform the most general class of functions to F 2 s. Our main contributions are twofold. First, we extend the subclass of submodular energy functions that can be minimized exactly using graph cuts. Second, we show how higher order potentials can be used to improve single view 3D reconstruction results. We believe that our work on exact minimization of higher order energy functions will lead to similar improvements in solutions of other labelling problems. 1.
Transformation of General Binary MRF Minimization to the First Order Case
 IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI
, 2011
"... Abstract—We introduce a transformation of general higherorder Markov random field with binary labels into a firstorder one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higherorder multilabel MRF energies that combines the new reduction ..."
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Cited by 29 (3 self)
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Abstract—We introduce a transformation of general higherorder Markov random field with binary labels into a firstorder one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higherorder multilabel MRF energies that combines the new reduction with the fusionmove and QPBO algorithms. While many computer vision problems today are formulated as energy minimization problems, they have mostly been limited to using firstorder energies, which consist of unary and pairwise clique potentials, with a few exceptions that consider triples. This is because of the lack of efficient algorithms to optimize energies with higherorder interactions. Our algorithm challenges this restriction that limits the representational power of the models so that higherorder energies can be used to capture the rich statistics of natural scenes. We also show that some minimization methods can be considered special cases of the present framework, as well as comparing the new method experimentally with other such techniques. Index Terms—Energy minimization, pseudoBoolean function, higher order MRFs, graph cuts. F 1
Energy Minimization for Linear Envelope MRFs
"... Markov random fields with higher order potentials have emerged as a powerful model for several problems in computer vision. In order to facilitate their use, we propose a new representation for higher order potentials as upper and lower envelopes of linear functions. Our representation concisely mod ..."
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Cited by 26 (8 self)
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Markov random fields with higher order potentials have emerged as a powerful model for several problems in computer vision. In order to facilitate their use, we propose a new representation for higher order potentials as upper and lower envelopes of linear functions. Our representation concisely models several commonly used higher order potentials, thereby providing a unified framework for minimizing the corresponding Gibbs energy functions. We exploit this framework by converting lower envelope potentials to standard pairwise functions with the addition of a small number of auxiliary variables. This allows us to minimize energy functions with lower envelope potentials using conventional algorithms such as BP, TRW and αexpansion. Furthermore, we show how the minimization of energy functions with upper envelope potentials leads to a difficult minmax problem. We address this difficulty by proposing a new message passing algorithm that solves a linear programming relaxation of the problem. Although this is primarily a theoretical paper, we demonstrate the efficacy of our approach on the binary (fg/bg) segmentation problem. 1.
Efficient Belief Propagation for HigherOrder Cliques Using Linear Constraint Nodes
 COMPUTER VISION AND IMAGE UNDERSTANDING
, 2008
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Interactive normal reconstruction from a single image
 ACM Transactions on Graphics
"... and two views of the reconstructed surface. We present an interactive system for reconstructing surface normals from a single image. Our approach has two complementary contributions. First, we introduce a novel shapefromshading algorithm (SfS) that produces faithful normal reconstruction for local ..."
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Cited by 16 (0 self)
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and two views of the reconstructed surface. We present an interactive system for reconstructing surface normals from a single image. Our approach has two complementary contributions. First, we introduce a novel shapefromshading algorithm (SfS) that produces faithful normal reconstruction for local image region (highfrequency component), but it fails to faithfully recover the overall global structure (lowfrequency component). Our second contribution consists of an approach that corrects lowfrequency error using a simple markup procedure. This approach, aptly called rotation palette, allows the user to specify large scale corrections of surface normals by drawing simple stroke correspondences between the normal map and a sphere image which represents rotation directions. Combining these two approaches, we can produce highquality surfaces quickly from single images. 1
Markov Random Field Modeling, Inference & Learning in Computer Vision & Image Understanding: A Survey
, 2013
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Optimizing binary MRFS with higher order cliques
, 2008
"... Abstract. Widespread use of efficient and successful solutions of Computer Vision problems based on pairwise Markov Random Field (MRF) models raises a question: does any link exist between the pairwise and higher order MRFs such that the like solutions can be applied to the latter models? This work ..."
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Cited by 11 (0 self)
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Abstract. Widespread use of efficient and successful solutions of Computer Vision problems based on pairwise Markov Random Field (MRF) models raises a question: does any link exist between the pairwise and higher order MRFs such that the like solutions can be applied to the latter models? This work explores such a link for binary MRFs that allow us to represent Gibbs energy of signal interaction with a polynomial function. We show how a higher order polynomial can be efficiently transformed into a quadratic function. Then energy minimization tools for the pairwise MRF models can be easily applied to the higher order counterparts. Also, we propose a method to analytically estimate the potential parameter of the asymmetric Potts prior. The proposed framework demonstrates very promising experimental results of image segmentation and can be used to solve other Computer Vision problems. 1